A125807 - OEIS

A125807

Central terms of odd-indexed rows of triangle A125806: a(n) = A125806(2n+1,n).

1, 3, 16, 119, 1070, 10762, 116546, 1330923, 15823388, 194168612, 2444224858, 31422225930, 411141476444, 5460849893348, 73474839110524, 999764999592077, 13738614091375204, 190450074950481408, 2660727794475865450

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OFFSET

0,2

COMMENTS

Central terms of even-indexed rows of triangle A125806 equal A063075 (number of partitions of 2n^2 whose Ferrers-plot fits within a 2n X 2n box and cover an n X n box).

LINKS

Table of n, a(n) for n=0..18.

PROG

(PARI) {a(n)=local(C_q=if(n==0, 1, prod(j=n+2, 2*n+1, 1-q^j)/prod(j=1, n, 1-q^j))); sum(i=0, (n+1)*n, polcoeff(C_q, i)^2)}

CROSSREFS

Cf. A125806 (triangle); A063075; A125808, A125809 (row sums).

Sequence in context: A190633 A220352 A333682 * A125222 A199670 A192783

Adjacent sequences: A125804 A125805 A125806 * A125808 A125809 A125810

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 12 2006

STATUS

approved